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Symmetries of nonmaximal supergravities with higher-derivative corrections
Phys. Rev. D 114, 026011 – Published 7 July, 2026
DOI: https://doi.org/10.1103/yj2x-v42c
Abstract
We consider hidden symmetries arising from U duality in the dimensional reduction of nonmaximal higher-derivative supergravities to three dimensions. In particular, we consider the symmetry of minimal five-dimensional supergravity and the symmetry of bosonic and heterotic string theory on . Using a group theory argument, we show that the higher-derivative corrections explicitly break all hidden symmetry enhancements. As special cases, this also implies that higher-derivative corrections prevent the symmetry enhancement to in pure five-dimensional gravity and in the STU model.
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References (81)
- J. Ehlers, Transformations of static exterior solutions of Einstein’s gravitational field equations into different solutions by means of conformal mapping, Colloq. Int. CNRS 91, 275 (1962).
- D. Maison, Ehlers-Harrison type transformations for Jordan’s extended theory of gravitation, Gen. Relativ. Gravit. 10, 717 (1979).
- D. Maison, Duality and hidden symmetries in gravitational theories, Lect. Notes Phys. 540, 273 (2000).
- J. Maharana and J. H. Schwarz, Noncompact symmetries in string theory, Nucl. Phys. B390, 3 (1993).
- A. Sen, Strong—weak coupling duality in four-dimensional string theory, Int. J. Mod. Phys. A 09, 3707 (1994).
- A. Sen, Strong—weak coupling duality in three-dimensional string theory, Nucl. Phys. B434, 179 (1995).
- E. Cremmer, B. Julia, H. Lu, and C. N. Pope, Dualization of dualities. 1., Nucl. Phys. B523, 73 (1998).
- E. Cremmer, B. Julia, H. Lu, and C. N. Pope, Dualization of dualities. 2. Twisted self-duality of doubled fields, and superdualities, Nucl. Phys. B535, 242 (1998).
- S. Cecotti, S. Ferrara, and L. Girardello, Geometry of type II superstrings and the moduli of superconformal field theories, Int. J. Mod. Phys. A 04, 2475 (1989).
- S. Mizoguchi and N. Ohta, More on the similarity between simple supergravity and M theory, Phys. Lett. B 441, 123 (1998).
- E. Cremmer, B. Julia, H. Lu, and C. N. Pope, Higher dimensional origin of coset symmetries, arXiv:hep-th/9909099.
- Z. W. Chong, M. Cvetic, H. Lu, and C. N. Pope, Charged rotating black holes in four-dimensional gauged and ungauged supergravities, Nucl. Phys. B717, 246 (2005).
- D. V. Gal’tsov and N. G. Scherbluk, Generating technique for U(1)**3 5D supergravity, Phys. Rev. D 78, 064033 (2008).
- D. V. Gal’tsov and N. G. Scherbluk, Improved generating technique for supergravities and squashed Kaluza-Klein Black Holes, Phys. Rev. D 79, 064020 (2009).
- G. Veneziano, Scale factor duality for classical and quantum strings, Phys. Lett. B 265, 287 (1991).
- K. A. Meissner and G. Veneziano, Symmetries of cosmological superstring vacua, Phys. Lett. B 267, 33 (1991).
- A. Sen, O(d) x O(d) symmetry of the space of cosmological solutions in string theory, scale factor duality and two-dimensional black holes, Phys. Lett. B 271, 295 (1991).
- A. Sen, Twisted black p-brane solutions in string theory, Phys. Lett. B 274, 34 (1992).
- M. Gasperini, J. Maharana, and G. Veneziano, From trivial to nontrivial conformal string backgrounds via O(d,d) transformations, Phys. Lett. B 272, 277 (1991).
- S. F. Hassan and A. Sen, Twisting classical solutions in heterotic string theory, Nucl. Phys. B375, 103 (1992).
- A. Sen, Rotating charged black hole solution in heterotic string theory, Phys. Rev. Lett. 69, 1006 (1992).
- M. Cvetic and D. Youm, All the four-dimensional static, spherically symmetric solutions of Abelian Kaluza-Klein theory, Phys. Rev. Lett. 75, 4165 (1995).
- M. Cvetic and D. Youm, All the static spherically symmetric black holes of heterotic string on a six torus, Nucl. Phys. B472, 249 (1996).
- M. Cvetic and D. Youm, General rotating five-dimensional black holes of toroidally compactified heterotic string, Nucl. Phys. B476, 118 (1996).
- A. Bouchareb, G. Clement, C.-M. Chen, D. V. Gal’tsov, N. G. Scherbluk, and T. Wolf, generating technique for minimal supergravity and black rings, Phys. Rev. D 76, 104032 (2007); 78, 029901(E) (2008).
- S. Tomizawa, Y. Yasui, and Y. Morisawa, Charged rotating Kaluza-Klein Black holes generated by transformation, Classical Quantum Gravity 26, 145006 (2009).
- G. Compere, S. de Buyl, E. Jamsin, and A. Virmani, Dualities in supergravity and black strings, Classical Quantum Gravity 26, 125016 (2009).
- R. Suzuki and S. Tomizawa, New construction of a charged dipole black ring by the Harrison transformation, Phys. Rev. D 109, 084020 (2024).
- R. Suzuki and S. Tomizawa, Solution generation of a capped black hole, Phys. Rev. D 110, 024026 (2024).
- R. Suzuki and S. Tomizawa, New black ring with all independent conserved charges in five-dimensional minimal supergravity, Phys. Rev. D 110, 124041 (2024).
- O. Hohm, A. Sen, and B. Zwiebach, Heterotic effective action and duality symmetries revisited, J. High Energy Phys. 02 (2015) 079.
- P.-J. Hu, L. Ma, Y. Pang, and R. J. Saskowski, Higher-derivative heterotic Kerr-Sen black holes, J. High Energy Phys. 02 (2026) 235.
- M. Xia, L. Ma, Y. Pang, and R. J. Saskowski, Consistent four-derivative heterotic truncations and the Kerr-Sen solution, Phys. Rev. D 113, 046019 (2026).
- C. M. Hull and P. K. Townsend, Unity of superstring dualities, Nucl. Phys. B438, 109 (1995).
- M. B. Green and M. Gutperle, Effects of D instantons, Nucl. Phys. B498, 195 (1997).
- M. B. Green and P. Vanhove, D instantons, strings and M theory, Phys. Lett. B 408, 122 (1997).
- M. B. Green, M. Gutperle, and P. Vanhove, One loop in eleven dimensions, Phys. Lett. B 409, 177 (1997).
- E. Kiritsis and B. Pioline, On R**4 threshold corrections in IIb string theory and (p, q) string instantons, Nucl. Phys. B508, 509 (1997).
- M. B. Green, M. Gutperle, and H.-h. Kwon, Sixteen fermion and related terms in M theory on T**2, Phys. Lett. B 421, 149 (1998).
- B. Pioline, A Note on nonperturbative R**4 couplings, Phys. Lett. B 431, 73 (1998).
- M. B. Green and S. Sethi, Supersymmetry constraints on type IIB supergravity, Phys. Rev. D 59, 046006 (1999).
- M. B. Green, H.-h. Kwon, and P. Vanhove, Two loops in eleven-dimensions, Phys. Rev. D 61, 104010 (2000).
- N. A. Obers and B. Pioline, Eisenstein series in string theory, Classical Quantum Gravity 17, 1215 (2000).
- A. Sinha, The G(hat)**4 lambda**16 term in IIB supergravity, J. High Energy Phys. 08 (2002) 017.
- N. Berkovits, Multiloop amplitudes and vanishing theorems using the pure spinor formalism for the superstring, J. High Energy Phys. 09 (2004) 047.
- E. D’Hoker and D. H. Phong, Two-loop superstrings VI: Non-renormalization theorems and the 4-point function, Nucl. Phys. B715, 3 (2005).
- E. D’Hoker, M. Gutperle, and D. H. Phong, Two-loop superstrings and -duality, Nucl. Phys. B722, 81 (2005).
- M. Matone and R. Volpato, Higher genus superstring amplitudes from the geometry of moduli space, Nucl. Phys. B732, 321 (2006).
- M. B. Green and P. Vanhove, Duality and higher derivative terms in M theory, J. High Energy Phys. 01 (2006) 093.
- M. B. Green, J. G. Russo, and P. Vanhove, Non-renormalisation conditions in type II string theory and maximal supergravity, J. High Energy Phys. 02 (2007) 099.
- A. Basu, The D**4 R**4 term in type IIB string theory on T**2 and U-duality, Phys. Rev. D 77, 106003 (2008).
- A. Basu, The D**6 R**4 term in type IIB string theory on T**2 and U-duality, Phys. Rev. D 77, 106004 (2008).
- M. R. Garousi, -duality constraint on higher-derivative couplings, J. High Energy Phys. 05 (2014) 100.
- J. R. Ellis and L. Mizrachi, Multiloop no renormalization theorems for the ten-dimensional heterotic string, Nucl. Phys. B327, 595 (1989).
- E. A. Bergshoeff and M. de Roo, The quartic effective action of the heterotic string and supersymmetry, Nucl. Phys. B328, 439 (1989).
- N. Lambert and P. C. West, Enhanced coset symmetries and higher derivative corrections, Phys. Rev. D 74, 065002 (2006).
- L. Bao, M. Cederwall, and B. E. W. Nilsson, Aspects of higher curvature terms and U-duality, Classical Quantum Gravity 25, 095001 (2008).
- C. Eloy, O. Hohm, and H. Samtleben, U duality and ’ corrections in three dimensions, Phys. Rev. D 108, 026015 (2023).
- J. T. Liu and R. J. Saskowski, Four-derivative corrections to minimal gauged supergravity in five dimensions, J. High Energy Phys. 05 (2022) 171.
- E. Cremmer, I. V. Lavrinenko, H. Lu, C. N. Pope, K. S. Stelle, and T. A. Tran, Euclidean signature supergravities, dualities and instantons, Nucl. Phys. B534, 40 (1998).
- A. Keurentjes, Poincare duality and G+++ algebra’s, Commun. Math. Phys. 275, 491 (2007).
- G. Bossard, H. Nicolai, and K. S. Stelle, Universal BPS structure of stationary supergravity solutions, J. High Energy Phys. 07 (2009) 003.
- J. Dixmier, Sur les représentations unitaires des groupes de lie nilpotents. III, Can. J. Math. 10, 321 (1958).
- J. T. Liu and R. J. Saskowski, Consistent truncations in higher derivative supergravity, J. High Energy Phys. 09 (2023) 136.
- W. H. Baron, D. Marques, and C. A. Nunez, Symmetry of Supergravity, Phys. Rev. Lett. 130, 061601 (2023).
- W. H. Baron, D. Marques, and C. A. Nunez, Exploring the symmetry of supergravity, J. High Energy Phys. 12 (2023) 006.
- N. Lambert and P. C. West, Duality groups, automorphic forms and higher derivative corrections, Phys. Rev. D 75, 066002 (2007).
- D. Robles-Llana, M. Rocek, F. Saueressig, U. Theis, and S. Vandoren, Nonperturbative corrections to 4D string theory effective actions from SL(2,Z) duality and supersymmetry, Phys. Rev. Lett. 98, 211602 (2007).
- S. Alexandrov, B. Pioline, F. Saueressig, and S. Vandoren, D-instantons and twistors, J. High Energy Phys. 03 (2009) 044.
- S. Alexandrov, D-instantons and twistors: Some exact results, J. Phys. A 42, 335402 (2009).
- T. Mohaupt, Black hole entropy, special geometry and strings, Fortschr. Phys. 49, 3 (2001).
- B. Pioline and E. Kiritsis, U duality and D-brane combinatorics, Phys. Lett. B 418, 61 (1998).
- N. A. Obers and B. Pioline, Eisenstein series and string thresholds, Commun. Math. Phys. 209, 275 (2000).
- B. Pioline, R**4 couplings and automorphic unipotent representations, J. High Energy Phys. 03 (2010) 116.
- M. B. Green, J. G. Russo, and P. Vanhove, Automorphic properties of low energy string amplitudes in various dimensions, Phys. Rev. D 81, 086008 (2010).
- M. B. Green, S. D. Miller, and P. Vanhove, Small representations string instantons, and Fourier modes of Eisenstein series, J. Number Theory 146, 187 (2015).
- G. Bossard and A. Kleinschmidt, Supergravity divergences, supersymmetry and automorphic forms, J. High Energy Phys. 08 (2015) 102.
- G. Bossard and A. Kleinschmidt, Loops in exceptional field theory, J. High Energy Phys. 01 (2016) 164.
- M. Ozkan, Y. Pang, and E. Sezgin, Higher derivative supergravities in diverse dimensions, Phys. Rep. 1086, 1 (2024).
- A. Pollack, Modular forms on and their standard -function, arXiv:1807.03884.
- M. B. Green, J. H. Schwarz, and L. Brink, Yang-Mills and supergravity as limits of string theories, Nucl. Phys. B198, 474 (1982).